Queuing-Inventory Models with MAP Demands and Random Replenishment Opportunities

Combining the study of queuing with inventory is very common and such systems are referred to as queuing-inventory in literature. These occur naturally practice have been studied extensively The considered literature generally include (s,S)-type. However, this paper we look at opportunistic-type replenishment which there an independent point process that used model events called opportunistic for replenishing inventory. When opportunity (to replenish) occurs, a probabilistic rule depends on level determine whether avail it or not. Assuming customers arrive according Markovian arrival process, demands batches varying size, require random service times modeled using continuous-time phase-type distribution, Poisson apply matrix-analytic methods two models. In one models, lost when arrivals no other model, can enter into system even if zero but server has be busy moment. idle completion epochs leave zero. Illustrative numerical examples presented, some possible future work highlighted.